How this calculator works
One radian subtends an arc as long as the radius. Dividing an arc length by its radius therefore gives the central angle in radians. Diameter input is halved first. Arc and radius can use different units because both convert to metres. Angles above one turn represent paths that wind around the circle more than once. A zero arc gives a zero angle, but it cannot determine a radius on its own.
Formula
theta = s/r; s = r theta; r = s/theta; d = 2r. These equations use theta in radians.
Worked example
An arc of length 2 pi metres on a circle of radius 2 metres subtends pi radians, or 180 degrees. With radius 4 metres, a 90 degree angle gives the same arc length.
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Frequently asked questions
Is this the same as an inscribed angle?
No. A central angle has its vertex at the circle's centre. An inscribed angle with the same intercepted arc is half the corresponding central angle.
Can the central angle exceed 360 degrees?
Yes when the arc describes a travelled path with multiple turns. For a single non-repeating arc of a circle, use an angle at most one turn.
Why can I not find a radius from a zero angle?
A zero angle has zero arc length for every radius. Dividing by zero cannot identify one circle size.